Design in nonlinear mixed effects models: optimization using the Fedorov-Wynn algorithm and power of the Wald test for binary covariates

We extend the methodology for designs evaluation and optimization in nonlinear mixed effects models with an illustration of the decrease of human immunodeficiency virus viral load after antiretroviral treatment initiation described by a bi-exponential model. We first show the relevance of the predicted standard errors (SEs) given by the computation of the population Fisher information matrix using the R function PFIM, in comparison to those computed with the stochastic approximation expectation-maximization algorithm, implemented in the Monolix software. We then highlight the usefulness of the Fedorov-Wynn (FW) algorithm for designs optimization compared to the Simplex algorithm. From the predicted SE of PFIM, we compute the predicted power of the Wald test to detect a treatment effect as well as the number of subjects needed to achieve a given power. Using the FW algorithm, we investigate the influence of the design on the power and show that, for optimized designs with the same total number of samples, the power increases when the number of subjects increases and the number of samples per subject decreases. A simulation study is also performed with the nlme function of R to confirm this result and show the relevance of the predicted powers compared to those observed by simulation.     

Electronic monitoring of variation in drug intakes can reduce bias and improve precision in pharmacokinetic/pharmacodynamic population studies

Population pharmacokinetic (PK) and pharmacodynamic (PD) studies evaluate drug concentration profiles and pharmacological effects over time when standard drug dosage regimens are assigned. They constitute a scientific basis for the determination of the optimal dosage of a new drug. Population PK/PD analyses can be performed on relatively few measures per patient enabling the study of a sizable sample of patients who take the drug over a possibly long period of time. We expose the problem of bias in PK/PD estimators in the presence of partial compliance with assigned treatment as it occurs in practice. We propose to solve this by recording accurate data on a number of previous dose timings and using timing-explicit hierarchical non-linear models for analysis. In practice, we rely on electronic measures of an ambulatory patient's drug dosing histories. Especially for non-linear PD estimation, we found that not only bias can be reduced, but higher precision can also be retrieved from the same number of data points when irregular drug intake times occur in well-controlled studies. We apply methods proposed by Mentré et al. to investigate the information matrix for hierarchical non-linear models. This confirms that a substantial gain in precision can be expected due to irregular drug intakes. Intuitively, this is explained by the fact that regular takers experience a relatively small range of concentrations, which makes it hard to estimate any deviation from linearity in the effect model. We conclude that estimators of PK/PD parameters can benefit greatly from information that enters through greater variation in the drug exposure process.     

A mixed effect model for bivariate meta‐analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution

Diagnostic test accuracy studies typically report the number of true positives, false positives, true negatives and false negatives. There usually exists a negative association between the number of true positives and true negatives, because studies that adopt less stringent criterion for declaring a test positive invoke higher sensitivities and lower specificities. A generalized linear mixed model (GLMM) is currently recommended to synthesize diagnostic test accuracy studies. We propose a copula mixed model for bivariate meta‐analysis of diagnostic test accuracy studies. Our general model includes the GLMM as a special case and can also operate on the original scale of sensitivity and specificity. Summary receiver operating characteristic curves are deduced for the proposed model through quantile regression techniques and different characterizations of the bivariate random effects distribution. Our general methodology is demonstrated with an extensive simulation study and illustrated by re‐analysing the data of two published meta‐analyses. Our study suggests that there can be an improvement on GLMM in fit to data and makes the argument for moving to copula random effects models. Our modelling framework is implemented in the package CopulaREMADA within the open source statistical environment R . Copyright © 2015 John Wiley & Sons, Ltd.